One control section at a time. MDOT has already done some of that south of Wiggins. I distinctly remember a reconstruction project near McHenry when I was stationed at Stennis.
What is a control section?
I may be wrong on this, I'm no engineer, but essentially its a section of roadway where access control is implemented. In the case of US 49 between Jackson and Gulfport, you could start with the rural sections of the highway first and implement grade seperations and access control, removing the crossovers and such.
Overall, MDOT has been actively improving 49 ever since Vision 21. Most recently, the widening from I-20 to Florence, and the addition of a southbound shoulder through Covington and Forrest/Stone counties. These safety projects have also eliminated a lot of the median crossovers.
Largely though, even as MDOT has made improvements, they've also signalized more intersections, such as MS 42 at US 49 and several stoplights through Collins. I remember driving through Collins at one point and only having 2 or 3 lights. Now there are 5 or so.
At this point it may be more cost effective to build a new facility. I've been of the opinion that a toll road authority should come in and construct a six-lane controlled access US 49 from I-20 to I-10 parallel to the existing US 49.